ZOOLOGY AND BOTAISIY, MICROSCOPY, ETC. 641 



the hundredth or a sixtieth of a turn can be recognized with greater 

 accuracy; otherwise the reading of the drum is merely illusory. If 

 the magnifying power of the Microscope is small, and the pitch of 

 the screw very shallow, the hundredth parts which are read are only 

 approximately true, and different results will be obtained from re- 

 peated observations, because the small size of the hundredths in the 

 image cannot be clearly distinguished. With stronger magnifying 

 power a screw of greater pitch can be used, and the hundredth parts can 

 be more clearly determined. With scale Microscopes of high power, the 

 micrometer divisions are more widely separated, and their tenths or 

 half-tenths can be estimated with proportionally greater accuracy. 

 The latter also possess, besides great simplicity, the advantage of rapid 

 reading. While, with the vernier and lens, it is necessary to search a 

 length of divisions for the coincident lines ; and with the screw Micro- 

 scope, the distance of the cross wire from the nearest division must be 

 measured by rotating and reading the screw-head ; with the scale Micro- 

 scope, a single glance is enough to show how many minutes, tenths, &c., 

 are to be added to the nearest division. 



Considering the accuracy attainable with scale Microscopes, and the 

 inconvenience attaching to screw Microscopes with their high power and 

 consequent loss of light, the latter must be regarded as inferior to the 

 former, unless means are devised for improving their optical character 

 to the same extent. 



In the author's opinion screw Microscopes are generally made too 

 long (and too heavy), in which there is no advantage, for, (1) the instru- 

 ment becomes large and inconvenient, and (2) the efficiency is not 

 increased, but diminished. In Microscopes used for scientific observa- 

 tions where the greatest efficiency and strongest magnifying power are 

 necessary, it has long been known that the best results are obtained 

 from powerful objectives combined with weak eye-pieces. Their short 

 focal length necessitates close approximation to the object, involving 

 increased aperture and greater intensity of light. Since, here as with 

 telescopes, increase of light means increased efficiency, this is of particular 

 importance in the present case where the object is opaque and cannot be 

 satisfactorily illuminated. But as with the telescope, so here in greater 

 degree, it is impossible to retain the same relation between focal 

 length and apertures for all focal lengths. Short focal lengths involve 

 much greater apertures than long ; both with a single objective lens 

 and with a compound system. Thus the most powerful dry systems 

 of 2 • 8 and 1 • 85 mm. equivalent focal lengths can have an aperture of 

 116°; while with 4*3 mm. focal length, the latter falls to 74°, with 

 7 mm. to 50°, with 11 mm. to 40°, with 18 mm. to 24°, and with 

 27 mm. to 20°. 



Half the aperture corresponds to one-quarter of the intensity of light; 

 the latter varies as the square of the former. From this it follows that 

 reading Microscopes with objectives of short focal length have the 

 advantage. Since they give brighter images, they can have stronger 

 magnifying power, and therefore greater efficiency, while at the same 

 time they are shorter and more convenient. 



To gain space for illumination, the objectives should consist of a 

 single aplanatic lens. The following table gives the most convenient 

 relation between aperture and focal length for such lenses. 



The aperture is slightly diminished by the fact that the object is 

 never strictly at the focus as is assumed in the table. 



